Multi-user hybrid analogue/digital beamforming for relatively large-scale antenna systems

Power consumption and costs of analogue front-end (AFE) chains are often not negligible for large-scale antenna array systems. A low-complexity hardware architecture is to use a number of AFE chains that are less than the number of antennas. Beamforming for this low-complexity hardware architecture involves both digital and analogue beamforming, which is termed hybrid analogue/digital beamforming. In this study, minimising the transmit power subject to signal-to-interference-plus-noise ratio (SINR) constraints and maximising the minimal SINR under the constraint of the transmit power, are investigated, respectively, for hybrid analogue/digital beamforming. Properties on the feasibility and optimality of the two problems are derived. Numerical algorithms based on semi-definite positive relaxation are proposed in an attempt to solve the two optimisation problems. The performance of the proposed algorithms is evaluated under the Gaussian and 60 GHz channel models. It is shown that the performance of hybrid analogue/digital beamforming is highly related to the correlation of the channel coefficients of subcarriers. Additionally, for different extents of the users' spatial separability, some heuristics ways of designing analogue beamforming are shown to be able to approach to at least the local optimums under the 60 GHz channel model.